Question 65711
The garden area is {{{30*20 = 600}}}
When the path around it is made, {{{400}}} is left
for the garden
If the width of the path is x, the area, {{{400}}}
is {{{(30 - 2x)*(20 - 2x)}}}
{{{(30 - 2x)*(20 - 2x) = 400}}}
{{{600 - 40x - 60x + 4x^2 = 400}}}
{{{4x^2 -100x + 200 = 0}}}
{{{x^2 - 25x + 50 = 0}}}
solve with quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-(-25) +- sqrt( (-25)^2-4*1*50 ))/(2*1) }}}
{{{x = (25 +- sqrt(625-200 ))/2 }}}
{{{x = (25 +- sqrt(425))/2 }}}
{{{x = (25 +- 20.616)/2}}}
{{{x = 12.5 - 10.308}}}
{{{x = 2.192}}} ft, answer
check
{{{(30 - 2x)*(20 - 2x) = 400}}}
{{{(30 - 2*2.192)*(20 - 2*2.192) = 400}}}
{{{(30 - 4.384)*(20 - 4.384) = 400}}}
{{{25.616*15.616 = 400}}}
{{{400 = 400}}}
Unless I goofed, that's it